Study sets matching "conics"

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Study sets matching "conics"

Conics
What is the Directrix ?
What is the Focus of a parabola?
Equation of Parabola in Standard Form
Equation of Parabola in Vertex Form
A fixed line that defines the parabola. Every point on the pa…
What is the Directrix ?
A fixed line that defines the parabola. Every point on the pa…
What is the Focus of a parabola?
26 terms
Conics
Equation of horizontal ellipse
Equation of vertical ellipse
Foci of horizontal ellipse
Directrices of horizontal ellipse
(+- C, 0)
x=a^2/c
Equation of horizontal ellipse
Equation of vertical ellipse
CONICS
how know if equation is a circle
how know if equation is a parabola
how know if equation is an elipse
how know if equation is a hyperbola
2 squared terms
1 squared term
2 squared terms = 1
2 squared terms and (-) sign
how know if equation is a circle
2 squared terms
how know if equation is a parabola
1 squared term
Conics
Circle
Standard Form of a Circle
Center of a Circle
Radius of a Circle
The set of all points that are equidistant from a point calle…
(x - h)2 + (y - k)2 = R2
(h , k)
R
Circle
The set of all points that are equidistant from a point calle…
Standard Form of a Circle
(x - h)2 + (y - k)2 = R2
Conics
Center of a Circle
Circle
Conic Section
Diameter
The point inside the circle that is the same distance from al…
The set of all points in a plane that are the same distance,…
A figure formed by the intersection of a plane and a right ci…
The distance across a circle through its center. The line seg…
Center of a Circle
The point inside the circle that is the same distance from al…
Circle
The set of all points in a plane that are the same distance,…
19 terms
Conics
What is the Directrix ?
What is the Focus of a parabola?
Equation of Parabola in Standard Form
Equation of Parabola in Vertex Form
A fixed line that defines the parabola. Every point on the pa…
What is the Directrix ?
A fixed line that defines the parabola. Every point on the pa…
What is the Focus of a parabola?
conics
vertical form for parabolas
focus for vertical form of a parabola
directrix vertical form of a parabola
to classify a conic what part of the e…
x2= 4py
(0, p)
y= -p
Ax2 + Bxy +Cy2
vertical form for parabolas
x2= 4py
focus for vertical form of a parabola
(0, p)
34 terms
Conics
Parabola
Point F
Line l
Vertex V
The set of points in the plane equidistant from the focus and…
Focus
Directrix
Lies halfway between the focus and the directrix
Parabola
The set of points in the plane equidistant from the focus and…
Point F
Focus
43 terms
Conics
The definition of a conic
The number of conics
Who invented the conics
The names of the conics
Graphs that are created by slicing a cone
4
Ancient Greeks
Parabola, circle, ellipse, hyperbola
The definition of a conic
Graphs that are created by slicing a cone
The number of conics
4
5 terms
Conics
ellipse
hyperbola vertical
circle
latus rectum
2b^2 / a
ellipse
hyperbola vertical
6 terms
Conics
Ellipse
Hyperbolas
Hyperbola Standard Form
Circle Standard Form
A set of points where the distance form any point (x,y) on th…
The set of all points that have the following characteristics…
Ellipse
A set of points where the distance form any point (x,y) on th…
Hyperbolas
The set of all points that have the following characteristics…
26 terms
Conics
circle
parabola
ellipse
hyperbola
coefficients same, both squared
only one variable squared
coefficients different, both squared & positive/negative
only one squared is negative
circle
coefficients same, both squared
parabola
only one variable squared
conics
parabola is when...
parabola x^2... parabola y^2
parabola vertical equation
parabola horizontal equation
either x or y is squared
vertical... horizontal
y-k = a(x-h)^2
x-h = a(y-k)^2
parabola is when...
either x or y is squared
parabola x^2... parabola y^2
vertical... horizontal
19 terms
Conics
Axis
Branch
Center
Circle
The line over which a parabola is symmetric.
The term for each of the two distinct sections of the graph o…
For an ellipse and hyperbola, the midpoint between the foci.…
The set of all points equidistant from a given fixed point.
Axis
The line over which a parabola is symmetric.
Branch
The term for each of the two distinct sections of the graph o…
Conics
Parabola
Circle
Ellipse
Hyperbola
Only one squared term
Same coefficient, same sign
Different coefficient, same sign
Different signs
Parabola
Only one squared term
Circle
Same coefficient, same sign
Conics
ellipse horizontal
ellipse vertical
circle
to find c of an ellipse
c2 = a2 - b2
ellipse horizontal
ellipse vertical
9 terms
Conics
unit circle
derivative of parametric equation
parametric equation
equations of an ellipse
unit circle
derivative of parametric equation
31 terms
Conics
Circle
Standard Form of a Circle
Center of a Circle
Radius of a Circle
The set of all points that are equidistant from a point calle…
(x - h)2 + (y - k)2 = R2
(h , k)
R
Circle
The set of all points that are equidistant from a point calle…
Standard Form of a Circle
(x - h)2 + (y - k)2 = R2
17 terms
conics
parabola is when...
parabola x^2... parabola y^2
parabola vertical equation
parabola horizontal equation
either x or y is squared
vertical... horizontal
y-k = a(x-h)^2
x-h = a(y-k)^2
parabola is when...
either x or y is squared
parabola x^2... parabola y^2
vertical... horizontal
24 terms
Conics
Form of an Equation:... y = a(x-h)^2 + k…
Form of an Equation:... x = a(y-k)^2 + h…
Vertex
Axis of Symmetry
Up if a > 0, down if a < 0
Right if a > 0, Left if a < 0
Always (h,k)
x=h in up/down parabola & y=k in right/left parabola
Form of an Equation:... y = a(x-h)^2 + k…
Up if a > 0, down if a < 0
Form of an Equation:... x = a(y-k)^2 + h…
Right if a > 0, Left if a < 0
Conics
distance formula
midpoint formula
ellipse formula
hyperbola formula
distance formula
midpoint formula
Conics
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1
(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1
(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1
Ellipse (left to right)
Ellipse (up and down)
Hyperbola (left and right sides)
Hyperbola ( top and bottom)
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Ellipse (left to right)
(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1
Ellipse (up and down)
Conics
ellipse horizontal
ellipse vertical
circle
to find c of an ellipse
c2 = a2 - b2
ellipse horizontal
ellipse vertical
33 terms
Conics
Circle
radius
Standard form of a circle
Center of circle
the set of all points in a plane that are equidistant from a…
the distance from the center to any point on the circle
(x-h)^2+(y-k)^2=r^2... or ... x^2+y^2=r^2
(h,k)
Circle
the set of all points in a plane that are equidistant from a…
radius
the distance from the center to any point on the circle
CONICS
m = tanA
tanA = (m2-m1)/(1+m2m1)
equal
It satisfies the equation
The angle of inclination
The angle of intersection between two lines
Vertical angles are...
If a point is on a conic, ...
m = tanA
The angle of inclination
tanA = (m2-m1)/(1+m2m1)
The angle of intersection between two lines
23 terms
Conics
x²+y²+4x−8y=0
x²-y²+4x-8y=0
2x²+2y²+4x-8y=0
2x²-2y²+4-8y=0
Circle
Hyperbola
Circle
Hyperbola
x²+y²+4x−8y=0
Circle
x²-y²+4x-8y=0
Hyperbola
5 terms
Conics
What is the difference between major a…
What is an equation of an ellipse?
Center of ellipse?
Distance from focus to ellipse?
(H,K)
Meaning of C
What is the difference between major a…
What is an equation of an ellipse?
14 terms
Conics
circle
midpoint formula
distance formula
parabola equation
(helps graph circles)
(helps graph circles)
opens up or down: (x-h)² =(+/-) 4p(y-k)... opens right or left:…
circle
midpoint formula
(helps graph circles)
Conics
unit circle
derivative of parametric equation
parametric equation
equations of an ellipse
unit circle
derivative of parametric equation
30 terms
Conics
Directrix of a up and down parabola
Focus of a up and down parabola
Equation of a up and down parabola
Directrix of a sideways parabola
y=k-p
(h, k+p)
(x-h)^2=4p(y-k)
x=h-p
Directrix of a up and down parabola
y=k-p
Focus of a up and down parabola
(h, k+p)
15 terms
Conics
distance formula
midpoint formula
standard form for a circle
domain and range of a circle
used to find diameter or radius when given 2 sets of points
used to find the center
x^2 + y^2 = r^2 OR (x-h)^2 + (y-k)^2 = r^2... x and y coefficie…
[brackets], domain - left to right, range - bottom to top
distance formula
used to find diameter or radius when given 2 sets of points
midpoint formula
used to find the center
6 terms
Conics
ellipse (submarine)
ellipse (pickle)
hyperbola (left/right)
hyperbola (up/down)
(x-h)²/b² + (y-k)²/a² = 1
ellipse (submarine)
ellipse (pickle)
(x-h)²/b² + (y-k)²/a² = 1
Conics
Ellipse
Circle
Parabola
Hyperbola
x^2/a^2 + y^2/b^2 = 1
x^2 + y^2 = r^2
x^2 = 4py
x^2/a^2 - y^2/b^2 = 1
Ellipse
x^2/a^2 + y^2/b^2 = 1
Circle
x^2 + y^2 = r^2
6 terms
Conics
Parabola
Ellipse
Hyperbola
Asymptote of hyperbolas when y is first
The set of all points in a plane that are equidistant from a…
Set of all points on a plane, the sum of whose distances from…
Set of all points in a plane, the difference of whose distanc…
y=k +/- a/b (x-h)
Parabola
The set of all points in a plane that are equidistant from a…
Ellipse
Set of all points on a plane, the sum of whose distances from…
6 terms
Conics
parabola: y=x^2
Parabola: x=y^2
Parabola: y=-x^2
Parabola: x=-y^2
Opens up
Opens to the right
Opens down
Opens left
parabola: y=x^2
Opens up
Parabola: x=y^2
Opens to the right
Conics
hyperbola equation
hyperbola asymptotes
hyperbola foci
ellipse equation
(x^2/a^2)-(y^2/b^2)=1... (y^2/b^2)-(x^2/a^2)=1
+-(b/a)x
(a+b)^1/2
(x^2/a^2)+(y^2/b^2)=1... (y^2/b^2)+(x^2/a^2)=1
hyperbola equation
(x^2/a^2)-(y^2/b^2)=1... (y^2/b^2)-(x^2/a^2)=1
hyperbola asymptotes
+-(b/a)x
Conics
locus
circle
ellipse
hyperbola
set of points that satisfy a given rule
a locus of points in a plane at a fixed distances,r, from a g…
locus of points in a plane for which the sum of the distances…
a locus of points in a plane for which the difference of the…
locus
set of points that satisfy a given rule
circle
a locus of points in a plane at a fixed distances,r, from a g…
Conics
circle
parabola
ellipse
hyperbola
coefficients same, both squared INCLUDING the sign
only one variable squared NOT both
when x and y are both squared and the coefficients are positi…
x and y are both squared and diff. signs
circle
coefficients same, both squared INCLUDING the sign
parabola
only one variable squared NOT both
conics
parabola equation
4p (parabola)
(h,k) (parabola)
if parabola faces sideways
(x-h)^2 = 4p (y-k)
directrix
vertex
(y-k)^2 = 4p (x-h)
parabola equation
(x-h)^2 = 4p (y-k)
4p (parabola)
directrix
10 terms
Conics
Circle
Parabola
Vertical Parabola
Horizontal Parabola
• (x-h)^2+(y-k)^2=r^2... • x^2 & y^2... • coefficient of x^2 & y^2…
only x^2 or y^2
y=a(x-h)^2+k
x=a(y-k)^2+h
Circle
• (x-h)^2+(y-k)^2=r^2... • x^2 & y^2... • coefficient of x^2 & y^2…
Parabola
only x^2 or y^2
Conics
Parabolas (horizontal, open side to si…
Parabolas (vertical, open up and down)
Ellipse (horizontally long)
Ellipse (vertically long)
(y-k)^2 = 4p(x-h)
(x-h)^2 = 4p(y-k)
(x-h)^2 / a^2 + (y-k)^2 / b^2 =1
(x-h)^2 / b^2 + (y-k)^2 / a^2 =1
Parabolas (horizontal, open side to si…
(y-k)^2 = 4p(x-h)
Parabolas (vertical, open up and down)
(x-h)^2 = 4p(y-k)
Conics
unit circle
derivative of parametric equation
parametric equation
equations of an ellipse
a^2 - b^2 = c^2
unit circle
derivative of parametric equation
17 terms
Conics
circle equation
Ellipse equation
Ellipse foci
hyperbola equation
(x-h)^2 + (y-k)^2 = r^2
(x-h/a)² + (y-k/b)² = 1
c^2=a^2-b^2... "c" units away
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
circle equation
(x-h)^2 + (y-k)^2 = r^2
Ellipse equation
(x-h/a)² + (y-k/b)² = 1
26 terms
Conics
Equation of horizontal ellipse
Equation of vertical ellipse
Foci of horizontal ellipse
Directrices of horizontal ellipse
(+- C, 0)
x=a^2/c
Equation of horizontal ellipse
Equation of vertical ellipse
22 terms
Conics
circle
Circle
center
radius
the intersection of a right circular cone with a plane that i…
the set of all points in a plane that are fixed distance from…
fixed point that is the same distance from all points on the…
segment whose endpoints are the center of the circle and a po…
circle
the intersection of a right circular cone with a plane that i…
Circle
the set of all points in a plane that are fixed distance from…
10 terms
Conics
Circle
Ellipse
Parabola: y =
Parabola: x =
Circle
Ellipse
19 terms
Conics
x^2=4py
y^2=4px
to find the equation of the tangent li…
in an ellipse, a is always the
opens left/right, parabola
opens up/down, parabola
distance formula with the focus point and the point on the pa…
longest/major axis
x^2=4py
opens left/right, parabola
y^2=4px
opens up/down, parabola
14 terms
Conics
Parabola
Parabola directrix
Parabola Foci
Circle
x^2,y x^2=4py
y=-p
(0,p)
(x-h)^2+(y-k)^2=r^2
Parabola
x^2,y x^2=4py
Parabola directrix
y=-p
5 terms
Conics
Equation of a circle
Equation of a hyperbola
Equation of a parabola
Equation of an elliptical
(X-x)^2 + (y-y)^2=r^2
(X-h)^2/a^2 - (y-k)^2/b^2 = 1
X=1/4p y^2
(X-h)^2 / a^2 + (y-k)^2 / b^2 =1
Equation of a circle
(X-x)^2 + (y-y)^2=r^2
Equation of a hyperbola
(X-h)^2/a^2 - (y-k)^2/b^2 = 1
10 terms
Conics
The ___ is the conic formed when the p…
The ___ comes from the Greek word that…
The ___ is the locus of points equidis…
A vicious ____ is a term from logic th…
parabola
parabola
parabola
circle
The ___ is the conic formed when the p…
parabola
The ___ comes from the Greek word that…
parabola
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